A mixture of taxonomy and nomenclatural comments here I think.
The author citation pins down the name as a nomenclatural object. Having it is especially useful for disambiguating homonyms, i.e. two names spelt the same, with different authors (or sometimes the same) but based on different type collection, ie different taxa.
Under the nomenclatural code only one such name can be valid/legitimate and the rest ignored. Most of the time most end-users of names (iNat included) do not need to know/see authors. They may appear usefully in statements of synonymy, but iNat doesn't serve synonymy. For a resource like iNat, or indeed any other database using names, the critical requirement is to be able to unambiguously link names together residing in different sources, so that data may be usefully integrated. In an ideal world we would have a single global catalogue of names of all organisms linked to permanent identifiers, and the identifiers would serve to link data. There continue to be attempts to do that at the global level. It is needed because 'name strings' with our without authors, are ineffective as stable unique identifiers. In the world of mycology the global nomenclator for all historical names is IndexFungorum, Mycobank iis based on a copy of the data contained in IndexFungorum. Both resources are also name registration centres and so both (try at least) to keep a synchronised complete set of names as new ones are minted. Both resources have web-services that can be used to look-up names and automatically retrieve data (including authors if required) but more importantly maintain the linkage between the resources based on those names. iNat uses such web-srevices, where avalailable, to retrieve name data from similar resources. I don't recall if it uses IndexFungorum in that way, but it could, and equivalently from MycoBank. It certainly uses our national digital species checklist in that way (NZOR) and that also maintains all the behind-the-scenes identifier linkages to resources like IndexFungorum, IPNI and so-on. There should not be no need to manually enter species names in iNat, or include authors to disambiguate homonyms. Finally, these resources are primarily nomenclators, ie databases of names and their standing under the codes. Taxonomic opinion about the correct use of a name to represent a taxon is a different issue. The iNat standard is to appeal to 'secondary sources' for that opinion. In the world of mycology it would be good if SpeciesFungorum or Mycobank served that role globally, but neither does an adequate job in that regard, in my opinion.